Lorenz_plot {L1centrality}

Lorenz Curve and the Gini Coefficient

Description

Draws a Lorenz curve (the group heterogeneity plot) and computes the Gini coefficient (the group heterogeneity index).

Usage

Lorenz_plot(x, add = FALSE, ...)

Arguments

x

A numeric vector.

add

A logical value.

• TRUE: add the Lorenz curve to an already existing plot.

• FALSE (the default): draw the Lorenz curve to a new graphic device.

...

Further graphical parameters supplied to the internal base::plot() (when add = FALSE) or graphics::lines() (when add = TRUE) function. See graphics::par() document.

Value

Draws a Lorenz curve (the group heterogeneity plot) and returns an invisible copy of a Gini coefficient (the group heterogeneity index).

References

S. Kang and H.-S. Oh. On a notion of graph centrality based on L₁ data depth. arXiv preprint arXiv:2404.13233, 2024.

M. O. Lorenz. Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70):209–219, 1905.

See Also

Use the function with L1cent() or L1centLOC(), and compare distributions of the centrality measurements across several groups and graphs.

Examples

vertex_weight <- igraph::V(MCUmovie)$worldwidegross
cent <- L1cent(MCUmovie, eta=vertex_weight)
gini <- Lorenz_plot(cent, asp=1)
graphics::abline(0,1,lty=2)
# group heterogeneity index
gini